The present invention relates generally to measurement of dielectric properties of thin films on substrates and, more specifically, to determination of the index of refraction and the dielectric constant of a thin polymer film on a substrate in the gigahertz (GHz) to terahertz (THz) frequency range.
In modern microcircuits, the high-frequency capacitance of interlevel dielectrics is a critical parameter that must be understood for realization of high-speed (clock speed greater than 1 GHz) electronic devices. The characterization of the high-frequency dielectric properties of interlevel dielectrics is thereby crucial, particularly in the gigahertz (GHz) to terahertz (THz) range. To bridge electronic and optical gaps formerly encountered in the measurement of the dielectric constant in the GHz-THz frequency range, time-domain spectroscopy (TDS) techniques that incorporate ultrashort laser pulses have been developed in recent years for microcircuit test devices.
For characterization of low dielectric constant materials before circuitization, however, a conventional free-space, non-contact measurement is the most convenient and low-cost method. For this purpose, a time-domain coherent technique has been demonstrated in the far-infrared (FIR) range that has been shown to be a promising alternative to the conventional electronic or continuous wave method. Boosted by the rapid development of a compact and portable femtosecond (fs) laser system, time-domain FIR techniques using all room-temperature components have become attractive for a number of industrial applications, including, but not limited to, gas spectroscopy, measurement of conductivity, study of the dynamics of semiconductor materials, and measurement of water concentration in biological samples. With extremely flat frequency response, large dynamic range, and excellent signal-to-noise ratio (SNR), free-space electro-optic sampling (FS-EOS) has emerged as a coherent terahertz detection technique capable of detecting amplitude, phase, and spacial distribution information in a terahertz beam. For example, the refractive index and dielectric constant of thin films has been measured by inserting the film into a THz beam and comparing the Fourier transforms of the THz waveforms obtained with and without the thin film.
For free-space dielectric constant measurement of the film on a substrate, where the thickness of the film is much thinner than the wavelength of the applied electromagnetic (EM) waves, the free-space time-domain technique has a fundamental restriction. The principle of the coherent free-space technique for measurement of the dielectric constant is based on the evaluation of the relative phase shift due to the index of refraction, the index of refraction being the square-root of the dielectric constant. For a film much thinner than the wavelength used for measurement, the visibility of the small phase shift in the waveform is difficult to obtain under realistic experimental conditions. For instance, for 100 GHz EM waves refracted through a one-micrometer film, a phase change on an order of only 10xe2x88x923 radians is expected. This phase difference is extracted by comparing a first waveform refracted through the thin film on a substrate against a second, reference waveform refracted from the substrate without the film. Under most experimental conditions, this extraction is often difficult due to the experimental uncertainty between two separate measurements. Thus, it is highly desirable to measure the phase difference in a single measurement.
U.S. Pat. No. 6,057,928, issued on May 2, 2000, to Ming Li et al., describes one method that avoids many of the problems in the prior art. That method requires measurements to be taken at multiple angles of reflection, however, which can be time consuming. The present invention proposes a differential time domain spectroscopy (DTDS) method that allows the measurement of dielectric properties on even thinner films and in less time than the method described in the ""928 patent.
The present invention provides a non-contact method for determining in a free space the index of refraction (n2(xcfx89)) at a desired angular frequency (xcfx89) of a sample comprising a thin, transmissive film which is optionally disposed on a substrate, the thin film having a thickness (d). The method comprises generating an input desired-frequency pulse and a probe pulse having wavelength and duration shorter than the input pulse, and directing the input pulse along a first path and the probe pulse along a second path. The sample is moved in and out of the first path, creating an output pulse which alternates between a transmitted signal (Efilm(xcfx89)), created when the sample is in the path of the input pulse, and a reference signal (Eref(xcfx89)), created when the sample is outside the input pulse path. The output pulse modulates the probe pulse, which is then detected with a photo detector, and a differential signal (Ediff(xcfx89)) for the thin film comprising a difference between the transmitted signal and the reference signal is calculated. The above steps are repeated over a plurality of delay times between the input pulse and the probe pulse until a complete field waveform of the differential signal for the thin film is characterized. The index of refraction is calculated as a function of a ratio between the differential signal for the thin film and the reference signal.
A complete field waveform of the reference signal may be characterized by repeating the above steps for a reference plate identical to the sample except comprising a non-transmissive film instead of the thin, transmissive film. Where the sample is mounted on a substrate, the non-transmissive film is mounted on an identical substrate. When repeating the above steps for the reference plate, the output pulse alternates between the reference signal (Eref(xcfx89)), created when the non-transmissive film is outside the path of the input pulse, and an absence of a signal, created when the non-transmissive film is in the path of the input pulse. The differential signal calculated for the reference plate is thus equal to the reference signal.
The index of refraction is calculated to be:
n2(xcfx89)={square root over ((n1+n3)(1+A(xcfx89)))xe2x88x92n1n3)}
where:       A    ⁢          (      ω      )        =            c              ω        ⁢                  xe2x80x83                ⁢        d              ⁢          "LeftBracketingBar"                                    E            diff                    ⁢                      (            ω            )                                                E            ref                    ⁢                      (            ω            )                              "RightBracketingBar"      
n1=index of refraction of the free space, and
n3=index of refraction of the optional substrate.
It is to be understood that both the foregoing general description and the following detailed description are exemplary, but are not restrictive, of the invention.